In Wideband Code Division Multiple Access (WCDMA) and other Direct Sequence-CDMA (DS-CDMA) systems, the current trend is towards higher rates via some combination of lower spreading factor, multi-code, higher-order modulation, and spatial multiplexing (MIMO). When the channel is dispersive, which is often the case at typical system bandwidths, some form of channel equalization is needed to provide adequate performance. Linear equalization techniques include “Generalized” Rake (G-Rake) and chip equalization. For an example of G-Rake processing, see Gregory E. Bottomley, et al., “A Generalized RAKE Receiver for Interference Suppression,” IEEE Journal on Selected Areas in Communications, Vol. 18, No. 8, August 2000. Linear equalization (in the frequency domain) has been proposed for the uplink of Long Term Evolution (LTE), a 3GPP standard that employs single-carrier, non-spread modulation.
Interest is also burgeoning in non-linear equalization techniques, including decision feedback equalization (DFE). Recently, there has been an effort to enhance DFE so that it performs better. One promising approach is bi-directional DFE (BD-DFE), in which the DFE is run either in the forward direction starting with the first symbol in a sequence of received symbols, or in the backward direction starting with the last symbol in the sequence.
More recently, BD-DFE has been performed by running both forward and backward directions and then further processing the results in some way. One way is arbitration, in which hard decision values from the two directions are selected based on a metric. See, for example, J. K. Nelson, et al., “BAD: Bidirectional arbitrated decision-feedback equalization,” IEEE Trans. Comm., vol. 53, no. 2, pp. 214-218, February 2005.
If the decisions made in the two directions of BD-DFE agree for a particular symbol, there is no need to compute and compare metrics. Where they disagree, a window of received values are considered, and a Euclidean distance metric is formed by comparing the received values to predicted values based on the symbol decisions and channel estimates. The direction which gives the best metric determines which direction to select for the symbol in the middle. Such “arbitration” processing has been extended to consider consecutive disagreeing symbol values, determining one metric for the group of symbols. See, for example, X.-G. Tang and Z. Ding, “Contradictory block arbitration for bi-directional decision feedback equalizers,” in Proc. IEEE Globecom, Nov. 17-21, 2002, pp. 283-286. Another interesting extension of BD-DFE uses the metric of a forward-error-correction (FEC) decoder to determine which symbol value to select. See, for example, H. S. Oh and D. S. Han, “Bidirectional equalizer arbitrated by Viterbi decoder path metrics,” IEEE Trans. Consumer Electronics, vol. 53, no. 1, pp. 60-64, February 2007.
While arbitration can provide significant performance gains over BD-DFE alone, these performance gains come at the expense of potentially significant increases in complexity. In general, DFE-based processing is more complex than linear equalization, such as in G-Rake and chip equalization. In particular, with arbitration-based DFE, the receiver must run DFE-based processing twice: once in the forward direction and once in the reverse direction. Further, the receiver needs to form potentially complex metrics for arbitration when the forward and backward direction results disagree.
Sequence estimation, e.g., Maximum Likelihood Sequence Estimation (MLSE), is another form of non-linear equalization, and it offers significant performance potential for reliably detecting sequences of symbols in a received signal. An MLSE process used for symbol detection processes a given sequence of symbols jointly. More particularly, an MLSE receiver processes received signal samples representative of a total sequence of symbols to be estimated, and produces a maximum likelihood (ML) estimate of the sequence. For one example of MLSE processing, see Gordon L. Stüber, Principles of Mobile Communication 364 (2nd ed. 2001). Further, see U.S. application Ser. No. 10/412,504, as filed by Wang et al. on 11 Apr. 2003, for examples of joint symbol detection, including MLSE-based detection. (Note that the Wang '504 application is co-owned with the instant application.)
Although inter-symbol interference (ISI) cancellation can be optimal with MLSE processing, computation complexity stands as a practical disadvantage of such processing. MLSE processing is particularly burdensome when used with extended sequence lengths and/or when used for estimating sequences of symbol vectors or blocks rather than sequences of individual symbols. (The number of possible symbol values per block is the number of combinations of possible symbol values for the individual symbols in the block.) Generally, the burden for MLSE processing increases significantly with the increasing number of possible paths (symbol vectors) represented by the sequence.
Several known techniques exist for increasing MLSE processing efficiency, such as by limiting sequence lengths—which can compromise estimation performance—and by “pruning” or otherwise eliminating certain paths during sequence estimation. In particular, the so-called “T Algorithm” and “M Algorithm” provide bases for path elimination during MLSE processing. For example, see U.S. Pat. No. 6,347,125 to Dent, which is co-owned with the instant application, for a brief discussion of the “M Algorithm” as used for complexity reduction in sequence estimation. Briefly, the M algorithm reduces the number of retained states by discarding those states with low likelihood metrics, meaning that the best M states are retained.